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2y^{''}-3y^'-2y=e^{2x}+x^2
2
y
′
′
−
3
y
′
−
2
y
=
e
2
x
+
x
2
y^{''}+2y^'-3y=e^{3x}(2+8x-12x^2)
y
′
′
+
2
y
′
−
3
y
=
e
3
x
(
2
+
8
x
−
1
2
x
2
)
y^{''}+20y^'+125y=9sin(5x)
y
′
′
+
2
0
y
′
+
1
2
5
y
=
9
sin
(
5
x
)
y^{''}+y^'-2y=e^t,y(0)=0,y^'(0)=1
y
′
′
+
y
′
−
2
y
=
e
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{''}+6y^'+9y= 1/x
y
′
′
+
6
y
′
+
9
y
=
1
x
x^{''}+4x^'+4x=100sin(4t)
x
′
′
+
4
x
′
+
4
x
=
1
0
0
sin
(
4
t
)
x^{''}+50x^'+400x=100cos(20t)
x
′
′
+
5
0
x
′
+
4
0
0
x
=
1
0
0
cos
(
2
0
t
)
y^{''}+y^'-2y=e^tsin(t),y(0)=0,y^'(0)=0
y
′
′
+
y
′
−
2
y
=
e
t
sin
(
t
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+22y^'+121y=16.3u
y
′
′
+
2
2
y
′
+
1
2
1
y
=
1
6
.
3
u
y^{''}+y=2e^{-8t},y(0)=0,y^'(0)=0
y
′
′
+
y
=
2
e
−
8
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{'''}-6y^'-7=0
y
′
′
′
−
6
y
′
−
7
=
0
(d^2y)/(dx^2)+9y=15x^2-9
d
2
y
dx
2
+
9
y
=
1
5
x
2
−
9
y^{''}+6y^'+8y=2t+e^t,y(0)=0,y^'(0)=0
y
′
′
+
6
y
′
+
8
y
=
2
t
+
e
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}-2y^'+y=(e^x)/x ,y(1)=0,y^'(1)=1
y
′
′
−
2
y
′
+
y
=
e
x
x
,
y
(
1
)
=
0
,
y
′
(
1
)
=
1
y^{''}+y^'+4y=e^{-1.3t}
y
′
′
+
y
′
+
4
y
=
e
−
1
.
3
t
y^{''}+3y^'+2y=3e^{-2x}+x
y
′
′
+
3
y
′
+
2
y
=
3
e
−
2
x
+
x
y^{''}-2y^'+y=30e^tt^{-7}
y
′
′
−
2
y
′
+
y
=
3
0
e
t
t
−
7
y^{''}+4y=12t
y
′
′
+
4
y
=
1
2
t
y^{''}-y^'+2y=2e^{2t}+5t-1
y
′
′
−
y
′
+
2
y
=
2
e
2
t
+
5
t
−
1
y^{''}+y^'+y=k
y
′
′
+
y
′
+
y
=
k
4y^{''}-y=e^{1/2 x}+7
4
y
′
′
−
y
=
e
1
2
x
+
7
(d^2y)/(dx^2)+2(dy)/(dx)-3y=x^2e^{-3x}
d
2
y
dx
2
+
2
dy
dx
−
3
y
=
x
2
e
−
3
x
y^{''}-y^'+y=2
y
′
′
−
y
′
+
y
=
2
y^{''}+3y^'-2=0
y
′
′
+
3
y
′
−
2
=
0
y^{''}+49y=-5cos(7t+pi^3),y(0)=0,y^'(0)=0
y
′
′
+
4
9
y
=
−
5
cos
(
7
t
+
π
3
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}-8y^'+16y=e^{4x}*ln(9+x^2)
y
′
′
−
8
y
′
+
1
6
y
=
e
4
x
·
ln
(
9
+
x
2
)
y^{''}-4y=(x-2)e^x
y
′
′
−
4
y
=
(
x
−
2
)
e
x
y^{''}+4y^'+3y=15
y
′
′
+
4
y
′
+
3
y
=
1
5
(D^2+1)y=sec^3(x)
(
D
2
+
1
)
y
=
sec
3
(
x
)
y^{''}-4y^'+3y=x,y(0)=6,y^'(0)=10
y
′
′
−
4
y
′
+
3
y
=
x
,
y
(
0
)
=
6
,
y
′
(
0
)
=
1
0
y^{''}+6y^'+25y=x^2
y
′
′
+
6
y
′
+
2
5
y
=
x
2
y^{''}+2y^'-8y=-650sin(3t)
y
′
′
+
2
y
′
−
8
y
=
−
6
5
0
sin
(
3
t
)
y^{''}+y^'+y=2
y
′
′
+
y
′
+
y
=
2
(d^2x)/(dt^2)+4(dx)/(dt)+4x=3sin(2t)
d
2
x
dt
2
+
4
dx
dt
+
4
x
=
3
sin
(
2
t
)
y^{''}+4y=cos(x),y(pi)=0,y(0)=0
y
′
′
+
4
y
=
cos
(
x
)
,
y
(
π
)
=
0
,
y
(
0
)
=
0
x^{''}-10x^'+25x=4te^{5t}
x
′
′
−
1
0
x
′
+
2
5
x
=
4
te
5
t
x^{''}+9x=2sin(t)
x
′
′
+
9
x
=
2
sin
(
t
)
y^{''}+2y^'=2
y
′
′
+
2
y
′
=
2
y^{''}+2y^'=7
y
′
′
+
2
y
′
=
7
y^{'''}-y^{''}-y^'+y=(1+e^{-x})
y
′
′
′
−
y
′
′
−
y
′
+
y
=
(
1
+
e
−
x
)
y^{''}-4y=(e^{2x}-e^{-2x})/2
y
′
′
−
4
y
=
e
2
x
−
e
−
2
x
2
(D^2+D+1)y=e^xsin(x)
(
D
2
+
D
+
1
)
y
=
e
x
sin
(
x
)
(d^2y)/(dx^2)+2(dy)/(dx)+y=e^{-x}
d
2
y
dx
2
+
2
dy
dx
+
y
=
e
−
x
y^{''}+9y=5sin(3x),y(0)=2,y^'(0)=0
y
′
′
+
9
y
=
5
sin
(
3
x
)
,
y
(
0
)
=
2
,
y
′
(
0
)
=
0
y^{''}+25y= 1/100 cos(5x)
y
′
′
+
2
5
y
=
1
1
0
0
cos
(
5
x
)
y^{''}+y^'-2y=3e^x
y
′
′
+
y
′
−
2
y
=
3
e
x
(d^2x)/(dt^2)-6(dx)/(dt)-7x=6
d
2
x
dt
2
−
6
dx
dt
−
7
x
=
6
1/6 y^{''}+6y=2tan(6t)-1/3 e^t
1
6
y
′
′
+
6
y
=
2
tan
(
6
t
)
−
1
3
e
t
y^{''}-y^'-2y=e^xcos(x)
y
′
′
−
y
′
−
2
y
=
e
x
cos
(
x
)
y^{''}+4y= t/2-(tcos(2t))/2
y
′
′
+
4
y
=
t
2
−
t
cos
(
2
t
)
2
y^{''}-7y^'-8y=8x^2-2x
y
′
′
−
7
y
′
−
8
y
=
8
x
2
−
2
x
x^{''}+4x^'+16x=4sin(2t)
x
′
′
+
4
x
′
+
1
6
x
=
4
sin
(
2
t
)
y^{''}+16y=cos(4t),y(0)=3,y^'(0)=2
y
′
′
+
1
6
y
=
cos
(
4
t
)
,
y
(
0
)
=
3
,
y
′
(
0
)
=
2
y^{''}-5y^'-6y=10
y
′
′
−
5
y
′
−
6
y
=
1
0
3(d^2y)/(dx^2)+20(dy)/(dx)+25y=cos(2x)
3
d
2
y
dx
2
+
2
0
dy
dx
+
2
5
y
=
cos
(
2
x
)
y^{'''}+3y^'-2x=0
y
′
′
′
+
3
y
′
−
2
x
=
0
(D^2+4D+5)y=e^{(-x)}+15x
(
D
2
+
4
D
+
5
)
y
=
e
(
−
x
)
+
1
5
x
y^{''}+y=2cos(x),y^'(pi)=0,y(0)=0
y
′
′
+
y
=
2
cos
(
x
)
,
y
′
(
π
)
=
0
,
y
(
0
)
=
0
(D^2+1)y=cos^2(x)
(
D
2
+
1
)
y
=
cos
2
(
x
)
(d^2y)/(dx^2)+6(dy)/(dx)+9y=xe^{-3x}
d
2
y
dx
2
+
6
dy
dx
+
9
y
=
xe
−
3
x
y^{''}+11y^'+18y=8\H(t)
y
′
′
+
1
1
y
′
+
1
8
y
=
8
H
(
t
)
y^{''}-y=t,y(0)=0,y^'(0)=0
y
′
′
−
y
=
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}-y=t,y(0)=0,y^'(0)=1
y
′
′
−
y
=
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{''}-4y^'+4y=x+e^x
y
′
′
−
4
y
′
+
4
y
=
x
+
e
x
y^{''}+y^'=2x+3
y
′
′
+
y
′
=
2
x
+
3
y^{''}-4y^'+4y=14x+5
y
′
′
−
4
y
′
+
4
y
=
1
4
x
+
5
y^{''}+10y^'+25y=e^{(-10x)/(x^2)}
y
′
′
+
1
0
y
′
+
2
5
y
=
e
−
1
0
x
x
2
d(r)=((ln(2)))/(ln(1+0.04))
d
(
r
)
=
(
ln
(
2
)
)
ln
(
1
+
0
.
0
4
)
y^{''}+y^'=2x-2
y
′
′
+
y
′
=
2
x
−
2
x^{''}-(pi^2)x=-1/pi
x
′
′
−
(
π
2
)
x
=
−
1
π
2y^{''}-4y^'-6y=16e^{-x}
2
y
′
′
−
4
y
′
−
6
y
=
1
6
e
−
x
2y^{''}-2y^'-4y=2e^3x
2
y
′
′
−
2
y
′
−
4
y
=
2
e
3
x
y^{''}-4y^'-12y=12t
y
′
′
−
4
y
′
−
1
2
y
=
1
2
t
y^{''}-2y^'+y=((e^t))/((1+t^2)+3e^t)
y
′
′
−
2
y
′
+
y
=
(
e
t
)
(
1
+
t
2
)
+
3
e
t
(d^2y)/(dx^2)-2(dy)/(dx)+y=x^{-2}e^x
d
2
y
dx
2
−
2
dy
dx
+
y
=
x
−
2
e
x
x^{''}+2x^'+5x=sin(2t)
x
′
′
+
2
x
′
+
5
x
=
sin
(
2
t
)
y^{''}-9y^'=3x^2-5sin(3x)
y
′
′
−
9
y
′
=
3
x
2
−
5
sin
(
3
x
)
y^{''}-y^'-2y=3e^{-x}
y
′
′
−
y
′
−
2
y
=
3
e
−
x
4y^{''}+16035y=4cos(8t)
4
y
′
′
+
1
6
0
3
5
y
=
4
cos
(
8
t
)
y^{''}+3y^'+2y=12e^t
y
′
′
+
3
y
′
+
2
y
=
1
2
e
t
D^2y=log_{10}(x)
D
2
y
=
log
1
0
(
x
)
y^{''}-2y^'-3y=3t^2
y
′
′
−
2
y
′
−
3
y
=
3
t
2
(D^2-2D+3)y=x^3+sin(x)
(
D
2
−
2
D
+
3
)
y
=
x
3
+
sin
(
x
)
(d^2y)/(dx^2)+9y=sec(3x)
d
2
y
dx
2
+
9
y
=
sec
(
3
x
)
y^{''}+2y^'+5y=e^xcos(2x)
y
′
′
+
2
y
′
+
5
y
=
e
x
cos
(
2
x
)
y^{''}+y=16cos(t),y(0)=0,y^'(0)=0
y
′
′
+
y
=
1
6
cos
(
t
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+9y=2x-5
y
′
′
+
9
y
=
2
x
−
5
(D^2+1)v=1
(
D
2
+
1
)
v
=
1
y^{''}-y^'+y=5sin(t)
y
′
′
−
y
′
+
y
=
5
sin
(
t
)
x^{''}+16x=144,x(0)=5,x^'(0)=12
x
′
′
+
1
6
x
=
1
4
4
,
x
(
0
)
=
5
,
x
′
(
0
)
=
1
2
y^{''}+3y^'-y=t,y(0)=0,y^'(0)=1
y
′
′
+
3
y
′
−
y
=
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
x^{''}+6x^'+9=0
x
′
′
+
6
x
′
+
9
=
0
y^{''}+4y=3,y^'(0)=0,y(0)=0
y
′
′
+
4
y
=
3
,
y
′
(
0
)
=
0
,
y
(
0
)
=
0
y^{''}-7/4 y^'+3/4 y=te^{2t}sin(-2t)
y
′
′
−
7
4
y
′
+
3
4
y
=
te
2
t
sin
(
−
2
t
)
x^{''}-x=-4e^{-t}
x
′
′
−
x
=
−
4
e
−
t
(d^2y)/(dx^2)+y=e^x
d
2
y
dx
2
+
y
=
e
x
y^{''}+y^'+6y=cos(2x)
y
′
′
+
y
′
+
6
y
=
cos
(
2
x
)
0.1x^{''}+10x=100sin(ct)
0
.
1
x
′
′
+
1
0
x
=
1
0
0
sin
(
ct
)
y^{''}-2y^'+y=x(cosh(x))
y
′
′
−
2
y
′
+
y
=
x
(
cosh
(
x
)
)
y^{''}-3y^'+2y=e^{3t},y(0)=-1,y^'(0)=-4
y
′
′
−
3
y
′
+
2
y
=
e
3
t
,
y
(
0
)
=
−
1
,
y
′
(
0
)
=
−
4
1
..
2361
2362
2363
2364
2365
..
2459